# Dictionary

## exponential notation

In physics, very large and very small numbers are written with the help of powers of the number ten. For large numbers, 10n with n a non-negative integer is a 1 with n trailing zeros:

100 = 1 = one
101 = 10 = ten
102 = 100 = a hundred
103 = 1000 = a thousand
106 = 1,000,000 = a million
109 = 1,000,000,000 = a billion
1012 = 1,000,000,000,000 = a trillion
1015 = 1,000,000,000,000,000 = a quadrillion

Very small fractions – numbers that differ very little from zero – can be written with the help of 10-n, with n a non-negative integer (n is, again, the number of zeros):

100 = 1 = one
10-1 = 0.1 = one tenth
10-2 = 0.01 = one hundredth
10-3 = 0.001 = one thousandth
10-6 = 0.000,001 = one millionths
10-9 = 0.000,000,001 = one billionths
10-12 = 0.000,000,000,001 = one trillionth
10-15 = 0.000,000,000,000,001 = one quadrillionth

Numbers that are not clean powers of ten can be written by factoring out the appropriate powers of ten. For instance,

1748 = 1.748·1000 = 1,748·103,

often written in what is called “scientific notation” as 1.748E3. On the other hand,

0.000,417,55 = 4.1755·10-4 = 4.1755E-4.